Ab initio computational study on the lattice thermal conductivity of Zintl clathrates [Si19 P4]Cl4 and Na4[Al4Si19]

The lattice thermal conductivity of silicon clathrate framework ${\mathrm{Si}}_{23}$ and two Zintl clathrates, $[{\mathrm{Si}}_{19}{\mathrm{P}}_{4}]{\mathrm{Cl}}_{4}$ and ${\mathrm{Na}}_{4}[{\mathrm{Al}}_{4}{\mathrm{Si}}_{19}]$, is investigated by using an iterative solution of the linearized Boltzmann transport equation in conjunction with ab initio lattice dynamical techniques. At 300 K, the lattice thermal conductivities for ${\mathrm{Si}}_{23}, [{\mathrm{Si}}_{19}{\mathrm{P}}_{4}]{\mathrm{Cl}}_{4}$, and ${\mathrm{Na}}_{4}[{\mathrm{Al}}_{4}{\mathrm{Si}}_{19}]$ were found to be 43 W/(m K), 25 W/(m K), and 2 W/(m K), respectively. In the case of ${\mathrm{Na}}_{4}[{\mathrm{Al}}_{4}{\mathrm{Si}}_{19}]$, the order-of-magnitude reduction in the lattice thermal conductivity was found to be mostly due to relaxation times and group velocities differing from ${\mathrm{Si}}_{23}$ and $[{\mathrm{Si}}_{19}{\mathrm{P}}_{4}]{\mathrm{Cl}}_{4}$. The difference in the relaxation times and group velocities arises primarily due to the phonon spectrum at low frequencies, resulting eventually from the differences in the second-order interatomic force constants (IFCs). The obtained third-order IFCs were rather similar for all materials considered here. The present findings are similar to those obtained earlier for some skutterudites. The predicted lattice thermal conductivity of ${\mathrm{Na}}_{4}[{\mathrm{Al}}_{4}{\mathrm{Si}}_{19}]$ is in line with the experimentally measured thermal conductivity of recently synthesized type-I Zintl clathrate ${\mathrm{Na}}_{8}[{\mathrm{Al}}_{8}{\mathrm{Si}}_{38}]$ (polycrystalline samples).